A Floquet Operator with Pure Point Spectrum and Energy Instability

TL;DR

This paper presents a specific Floquet operator that exhibits pure point spectrum and energy instability, with eigenfunctions that are exponentially localized in the unperturbed energy basis.

Contribution

It introduces a Floquet operator with unique spectral properties and energy instability, expanding understanding of quantum dynamical systems.

Findings

Floquet operator has purely point spectrum

Eigenfunctions are exponentially localized

Energy instability is demonstrated

Abstract

An example of Floquet operator with purely point spectrum and energy instability is presented. In the unperturbed energy eigenbasis its eigenfunctions are exponentially localized.